bibkey: ali2019qutritfreezing
authors: Mazhar Ali
year: 2019
title: "Freezing dynamics of entanglement and nonlocality for qutrit-qutrit (3 ⊗ 3) quantum systems"
doi: 10.1142/s0217732319501025
url: https://arxiv.org/abs/1810.01123v1
claim: "For two qutrits under Markovian collective dephasing, the paper studies the negativity of a mixed family and of random pure states, observes freezing dynamics, and conjectures that time-invariant entanglement, in which the state changes while its entanglement stays constant, may not exist under this dynamics."
strata_touched:
  - D5/S3/Quantum/Decoherence/QutritCollectiveDephasingInvariantNegativityRefutation
license: citation-only
triage: anchor

Freezing dynamics of entanglement and nonlocality for qutrit-qutrit (3 ⊗ 3) quantum systems

Mazhar Ali, arXiv:1810.01123v1 (quant-ph), 2018-10-02; published in Mod. Phys. Lett. A 34, 1950102 (2019). Quotations are from the v1 TeX source.

The feature (Introduction):

Time-invariant entanglement does not necessarily mean that the quantum states live in decoherence free subspaces (DFS). In fact the quantum states may change at every instance whereas their entanglement remain constant throughout the dynamical process.

The dynamics (Section II):

\rho(t) = , \sum_{k=1}^3 , (D_k^{AB , \dagger} , \rho(0) , D_k^{AB}), , \label{Eq:GS} \end{eqnarray} where the terms describing interaction with collective magnetic field $B(t)$ involve the operators $D_1^{AB}=\mathrm{diag}(\gamma (t),1,1,1,\gamma (t),1,1,1,\gamma (t))$, $D_2^{AB}=\mathrm{diag}({\omega }_1(t),0,0,0,{\omega }_2(t),0,0,0,{\omega }_2(t))$, and $D_3^{AB}=\mathrm{diag}(0,0,0,0,{\omega }_3(t),0,0,0,{\omega }_3(t))$. The time dependent parameters are defined as, $\gamma ={\mathrm{e}}^{-\Gamma t/2}$, ${\omega }_1(t)=\sqrt{1-{\gamma }^2(t)}$, ${\omega }_2(t)=-{\gamma }^2(t)\sqrt{1-{\gamma }^2(t)}$, and ${\omega }_3(t)=(1-{\gamma }^2(t))\sqrt{1+{\gamma }^2(t)}$.

The entanglement measure (Section III):

Negativity \cite{Vidal-PRA65-2002} is a useful measure to quantify entanglement of bipartite NPT states

The conjecture (Section V, Conclusions):

We have found no evidence for time-invariant entanglement for qutrit-qutrit states and based on our results, we conjecture that under current dynamics, this feature of time-invariant entanglement may not exist for qutrit-qutrit systems.

Verified locator

• URL: https://arxiv.org/abs/1810.01123v1 (v1, 2018-10-02; source Ali-PLA-Efreezing.tex, md5 bdcb531e2cf6e54368bb8cdcb63b7d0e): the feature (l. 53–54), the dynamics (l. 117–124), negativity (l. 193), and the conjecture (l. 386–387).
• DOI: 10.1142/s0217732319501025 (Mod. Phys. Lett. A 34, 1950102; publication date 2019-03-27 per OpenAlex W2895233168). The published text was not read.